Modified THDRK methods for the numerical integration of the Schrödinger equation-Reference-Cited by-同舟云学术

Modified THDRK methods for the numerical integration of the Schrödinger equation

Published:2020-09-23 Issue:10 Volume:31 Page:2050149
ISSN:0129-1831
Container-title:International Journal of Modern Physics C
language:en
Short-container-title:Int. J. Mod. Phys. C

Author:

Fang Yonglei¹,Yang Yanping¹,You Xiong²,Ma Lei³

Affiliation:

1. School of Mathematics and Statistics, Zaozhuang University, Zaozhuang 277160, P. R. China

2. Department of Applied Mathematics, Nanjing Agricultural University, Nanjing 210095, P. R. China

3. School of Optoelectronic Engineering, Zaozhuang University, Zaozhuang 277160, P. R. China

Abstract

Modified three-derivative Runge–Kutta (MTHDRK) methods for the numerical solution of the resonant state for the Schrödinger equation are investigated. Order conditions are presented and oscillation-fitting conditions are derived. Two practical fifth-order explicit MTHDRK methods are constructed and the error analysis is carried out for large energy. The numerical results are presented for the numerical solution of the Schrödinger equation to show the robustness of our new methods.

Funder

the Natural Science Foundation of China

the Natural Science Foundation of Shandong Province, China

the Natural Science Foundation of Jiangsu Province, China

the Foundation of Innovative Science and Technology for Youth in Universities of Shandong Province

Publisher

World Scientific Pub Co Pte Lt

Subject

Computational Theory and Mathematics,Computer Science Applications,General Physics and Astronomy,Mathematical Physics,Statistical and Nonlinear Physics

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0129183120501491

Reference22 articles.

1. AN EMBEDDED RUNGE–KUTTA METHOD WITH PHASE-LAG OF ORDER INFINITY FOR THE NUMERICAL SOLUTION OF THE SCHRÖDINGER EQUATION

2. A variable-step Numerov method for the numerical solution of the Schr�dinger equation

3. ON THE CONSTRUCTION OF EFFICIENT METHODS FOR SECOND ORDER IVPS WITH OSCILLATING SOLUTION

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